Flow behaviour

Dynamic viscosity η

Looking at two parallel plates with the surface A and the distance y, displaced against each other as a result of a force Faction with a velocity v, a force Freaction opposes to this displacement and increases with increasing dynamic viscosity of the medium between the two plates. (fig 1)

The ratio of F to A is called shear stress τ.

τ = F / A

The shear stress τ increases in proportion to the shear velocity D and the dynamic viscosity η.

τ = D x η

The ratio of v to y is defined as shear velocity D.

D = v / y

Thus the resulting dynamic viscosity η:

η = τ / D

Thus, the dynamic viscosity η is a characteristic parameter of the fluid concerned and depends on the temperature. Therefore the viscosity is always indicated together with the corresponding temperature.

With a Reynolds number of 2320 the laminar flow passes to a turbulent flow.

Laminar flow < Rekrit = 2320 < turbulent flow

Example:
In one second, 2 litres of acetic acid passes through a pipe with a nominal bore of 50 mm.
The acetic acid has a dynamic viscosity of η = 1.21 mPa s = 0.00121 Pa s and a density of 1.04 kg/dm3.
Is the flow laminar or turbulent?

The average flow velocity amounts to:

Q [l/s]

v = Q / A = Q / (¼ πd2) = (2 * 1000) / (502 * π / 4) = 1.02 m/s

d [mm]

v [m/s]

Thus the calculated Reynolds number is:

Re = (v * d * ρ) / η = (1.02 * 50 * 1.04) / 0.00121 = 43834

The Reynolds number exceeds the critical Reynolds number Rekrit=2320. The flow is turbulent.

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